"Gabriel's theorem"의 두 판 사이의 차이

2021년 2월 17일 (수) 01:06 기준 최신판

statement

thm (Gabriel)

A connected quiver Q has finite type iff the underlying graph is a Dynkin diagram of (A,D,E) type. Moreoever there is a bijection between {indecomposable kQ-modules} and {positive roots} \[M \to \dim M\] where \(\dim\) is dimension vector

idea of proof

define tilting functor
get Coxeter element

Kac theorem

related items

expositions

Carroll, Gabriel's Theorem

메타데이터

위키데이터

ID : Q5515505

Spacy 패턴 목록

[{'LOWER': 'gabriel'}, {'LOWER': "'s"}, {'LEMMA': 'theorem'}]

@@ 1번째 줄: / 1번째 줄: @@
 ==statement==
-* \thm (Gabriel)
+;thm (Gabriel)
-*  A connected quiver Q has finite type iff the underlying graph is a Dynkin diagram of (A,D,E) type. Moreoever there is a bijection<br> {indecomposable kQ-modules} -> {positive roots}<br> M -> dim M (dimension vector)<br>
+A connected quiver Q has finite type iff the underlying graph is a Dynkin diagram of (A,D,E) type. Moreoever there is a bijection between {indecomposable kQ-modules} and {positive roots}
+:<math>M \to \dim M</math>
+where <math>\dim</math> is dimension vector
 ==idea of proof==
@@ 13번째 줄: / 16번째 줄: @@
 * get Coxeter element
+==Kac theorem==
-==Kac theorem==
+==related items==
+* [[Quiver representations]]
+* [[Coxeter functor and transformation]]
+==expositions==
+* Carroll, [http://www.math.missouri.edu/~carrollat/files/Quiver_Lecture.pdf Gabriel's Theorem]
+[[분류:개인노트]]
+[[분류:cluster algebra]]
+[[분류:math and physics]]
+[[분류:math]]
+[[분류:migrate]]
-*
+==메타데이터==
+===위키데이터===
+* ID :  [https://www.wikidata.org/wiki/Q5515505 Q5515505]
+===Spacy 패턴 목록===
+* [{'LOWER': 'gabriel'}, {'LOWER': "'s"}, {'LEMMA': 'theorem'}]